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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Use of Physics to Improve Solar Forecast: Physics-Informed Persistence Models for Simultaneously Forecasting GHI, DNI, and DHI

Observation-based statistical models have been widely used in forecasting solar energy; however, existing models often lack a clear relation to physics and are limited largely to global horizontal irradiance (GHI) forecasts over relatively short time horizons (< 1 hour). Incorporating physics into observation-based models, increasing forecast time horizons and developing a model system for forecasting not only GHI but also direct normal irradiance (DNI) and diffuse horizontal irradiance (DHI) remain challenging, especially under cloudy conditions because of complex cloud-radiation interactions. This work attempts to address these challenges by developing a hierarchy of four new physics-informed persistence models that can be used to simultaneously forecast GHI, DNI and DHI. The decade-long measurements (1998 to 2014) at the U.S. Department of Energy's Atmospheric Radiation Measurement (ARM)'s Southern Great Plains (SGP) Central Facility site are used to evaluate the performance of the new models. Overall, the results show that the new physics-informed forecast models generally outperform the simple and smart persistence models, and improve the forecast accuracy at lead times from 1.25 hours up to 6 hours. Further analysis reveals that the forecast error is highly related to the error and temporal variability of the assumed cloud predictor. The best model for forecasting different radiative components can be explained by the relationship between solar irradiances and cloud properties.

54 ENVIRONMENTAL SCIENCES↗
NASA NTRS1991

Surface wind convergence as a short-term predictor of cloud-to-ground lightning at Kennedy Space Center: A four-year summary and evaluation

Since 1986, USAF forecasters at NASA-Kennedy have had available a surface wind convergence technique for use during periods of convective development. In Florida during the summer, most of the thunderstorm development is forced by boundary layer processes. The basic premise is that the life cycle of convection is reflected in the surface wind field beneath these storms. Therefore the monitoring of the local surface divergence and/or convergence fields can be used to determine timing, location, longevity, and the lightning hazards which accompany these thunderstorms. This study evaluates four years of monitoring thunderstorm development using surface wind convergence, particularly the average over the area. Cloud-to-ground (CG) lightning is related in time and space with surface convergence for 346 days during the summers of 1987 through 1990 over the expanded wind network at KSC. The relationships are subdivided according to low level wind flow and midlevel moisture patterns. Results show a one in three chance of CG lightning when a convergence event is identified. However, when there is no convergence, the chance of CG lightning is negligible.

Watson, Andrew I.↗
NASA NTRS1991

Surface wind convergence as a short-term predictor of cloud-to-ground lightning at Kennedy Space Center

Cloud-to-ground lightning is a significant forecast problem at the Kennedy Space Center (KSC) in Florida. In this study, cloud-to-ground lightning is related in time and space to surface convergence for 244 days during the convective seasons of 1985 and 1986 over a 790 sq-km network at KSC. The method uses surface convergence, particularly the average over the area, to identify the potential for new, local thunderstorm growth, and it can be used to specify the likely time and location of lightning during the life cycle of the convection. A threshold of 75 x 10 to the -6th/s change in divergence is the main criterion used to define a convergence event, and a set of flashes less than 30 min apart defines a lightning event. Time intervals are found from the study to be approximately 1 h from beginning convergence to first flash, and another hour to the end of lightning. The influences of low-level winds and midlevel moisture in determining the location and intensity of convection are discussed. This is the first known dynamically-based forecast method for lightning prediction. The technique, currently in use at KSC, has been shown to be a systematic, quantitative tool for predicting lightning onset in situations where conventional analysis tools such as radar and satellite are limited.

Watson, Andrew I.↗
DOE OSTI2025

A Novel Thermodynamical Predictor of Tropical High‐Cloud Area Coverage: Estimated Anvil‐Outflow Stability

The stability at the lapse-rate tropopause (LRT) was previously defined as the upper-tropospheric stability (UTS and SUT) but might underestimate the stability control on high-level clouds, since there is little direct connection between convective processes and the thermal stratification at the LRT. Here, a novel estimated anvil-outflow stability (EAS) based on the minimum stability in the upper troposphere is proposed. At the Manus site, the results show that small and large values of the LRT-based UTS and SUT both correspond to strong divergence and frequent occurrence of high-level ice clouds. In contrast, smaller EAS corresponds to stronger convective outflows to produce likely more high-level ice clouds, with a strong negative correlation. In tropics, EAS better explains the geographic distribution of high-level cloud coverage (HCC) and its temporal variations than UTS and SUT. With a strong linear correlation, EAS is likely a simple useful predictor of HCC.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2020

On the Relationship Between the Marine Cold Air Outbreak M Parameter and Low-Level Cloud Heights in the Midlatitudes

Focusing on conditions of subsidence when low clouds are present, ground-based observations in both the North Atlantic and the Southern Ocean reveal strong relationships between cloud boundary (base and top heights) and different measures of lower tropospheric instability. The difference in potential temperature between the surface and 800 hPa (a metric called M) provides a stronger relationship than measures of inversion strength such as the lower tropospheric stability and estimated inversion strength. This is because (1) inversion strength itself does not correlate well with cloud boundaries, and (2) M contains information that appears important for cloud boundaries. These include the surface forcing through the use of sea surface rather than near-surface air temperature and an upper level close to the real cloud top. These results expand upon previous work on the importance of M as a predictor of cloud morphology. However, important differences are found in low-cloud conditions for the North Atlantic as compared to the Southern Ocean (for a given value of M): stronger inversions, deeper boundary layers, and much larger sea level pressures. Therefore, the relationship between cloud boundaries and M differs between the two regions. A general circulation model provides similar relationships as observed between M and both cloud top height and temperature but tends to place clouds higher and at colder temperatures than observed for a given M. This might cause issues with the representation of precipitation, cloud cover and radiation in the Southern Ocean.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2021

Improving Prediction of Surface Solar Irradiance Variability by Integrating Observed Cloud Characteristics and Machine Learning

A 5-year, 1-minute resolution observational dataset of clouds and solar radiation was produced that includes two metrics of the variability in surface solar irradiance due to cloud type and fractional sky cover. Multiple regression models were trained to fit observations of surface solar irradiance variability from those two cloud property predictors. We found that ensemble tree-based methods, Random Forest and Gradient Boosting Machine, have the least overfitting issues and showed the best performance with an R2 of 0.42. While the observational data trained in this study was only from one site, the U.S. Department of Energy (DOE) Atmospheric Radiation Measurement (ARM) Southern Great Plains (SGP) site in Oklahoma, initial comparisons of the seasonality of the statistics suggest that these results are relatively weather regime independent; the generality of such a finding across sites will be tested in future work. The observational data and developed machine learning model are being used to create a numerical weather prediction model parameterization to enable day-ahead solar variability prediction in a computationally efficient way. This is a first step towards creating a new paradigm of predicting day-ahead variability with the potential to provide a new tool to improve grid operation, planning, and resilience.

Riihimaki, Laura↗
NASA NTRS1989

Use of the surface wind field as a predictor of thunderstorms and cloud-to-ground lightning at Kennedy Space Center

The convergence-lightning nowcasting method that began to be operationally tested and evaluated by USAF personnel at the KSC in 1986 uses surface convergence, especially the areal average, to identify the potential for new thunderstorm growth. When this areal method fails, normalized cell convergence, which is defined as the integral of cellular convergence with respect to its area, can be used as a complementary technique in association with the areal one. A detailed examination is conducted for one day, and the relationship of normalized cell convergence to lightning flash counts is examined in a 68-day ensemble.

Watson, Andrew I.↗
NASA NTRS1993

Investigation of cloud/water vapor motion winds from geostationary satellite

Work has been primarily focussed on three tasks: (1) comparison of wind fields produced at MSFC with the CO2 autowind/autoeditor system newly installed in NESDIS operations; (2) evaluation of techniques for improved tracer selection through use of cloud classification predictors; and (3) development of height assignment algorithm with water vapor channel radiances. The contract goal is to improve the CIMSS wind system by developing new techniques and assimilating better existing techniques. The work reported here was done in collaboration with the NESDIS scientists working on the operational winds software, so that NASA funded research can benefit NESDIS operational algorithms.

Nieman, Steve↗
DOE OSTI2023

Vertical Structure and Ice Production Processes of Shallow Convective Postfrontal Clouds over the Southern Ocean in MARCUS. Part I: Observational Study

A study of the vertical structure of postfrontal shallow clouds in the marine boundary layer over the Southern Ocean is presented here. The central question of this two-part study regards cloud phase (liquid/ice) of precipitation, and the associated growth mechanisms. In this first part, data from the Measurements of Aerosols, Radiation, and Clouds over the Southern Ocean (MARCUS) field campaign are analyzed, starting with a 75-h case with continuous sea surface-based thermal instability, modest surface heat fluxes, an open-cellular mesoscale organization, and very few ice nucleating particles (INPs). The clouds are mostly precipitating and shallow (tops mostly around 2 km above sea level), with weak up- and downdrafts, and with cloud-top temperatures generally around –18° to –10°C. Further, the case study is extended to three other periods of postfrontal shallow clouds in MARCUS. While abundant supercooled liquid water is commonly present, an experimental cloud-phase algorithm classifies nearly two-thirds of clouds in the 0° to –5°C layer as containing ice (cloud ice, snow, or mixed phase), implying that much of the precipitation grows through cold-cloud processes. The best predictors of ice presence are cloud-top temperature, cloud depth, and INP concentration. Measures of convective activity and turbulence are found to be poor indicators of ice presence in the studied environment. The water-phase distribution in this cloud regime is explored through numerical simulations in Part II. Significance Statement: Climate models generally predict a lower albedo than observed over the Southern Ocean, and this is largely attributed to a lack of cloudiness, especially in the postfrontal cold sector of midlatitude cyclones. This in turn may be due to an excess of ice in these simulated clouds, resulting in rapid precipitation fallout and an overly brief cloud lifespan. The objective of this study is to examine whether shallow postfrontal clouds over the Southern Ocean are dominated by supercooled drops, or by snow and ice, using data collected by a U.S. Department of Energy Atmospheric Radiation Measurement Mobile Facility deployed aboard an Australian Antarctic supply vessel. We find that these clouds contain much supercooled liquid, even though cloud-top temperatures generally are around –18° to –8°C, and that about two-thirds of the clouds just above the freezing level contain ice. Much of the precipitation appears to grow through cold-cloud processes above the freezing level, rather than drizzle/rain. Updrafts and/or turbulence in convection or in cloud-top generating cells do not initiate much ice, compared to observations elsewhere in a similar temperature range. This may be attributable to the extremely low concentration of ice nucleating particles in this environment. Ultimately, the deepest clouds with the coldest cloud tops are most likely to be ice dominated.

54 ENVIRONMENTAL SCIENCES↗
NASA NTRS2022

Deriving Severe Hail Likelihood from Satellite Observations and Model Reanalysis Parameters using a Deep Neural Network

Geostationary satellite imagers, such as those of the Geostationary Operational Environmental Satellite (GOES) series, have been observing severe convection at 15–60-minute intervals for over 40 years. When properly assessed, such a data record can be valuable in efforts of estimating severe storm risk throughout the diurnal cycle based on automated detection of patterns consistently found atop severe storms. Furthermore, environmental conditions favorable for severe weather are well-known and are thought to be represented well by modern reanalysis products. Promoting resilience against such hazards on local and global scales is a chief goal the NASA Disasters program, which seeks to encourage use of satellite observations to mitigate risk. For instance, hail is the costliest severe weather hazard across the globe in terms of insured loss, but reporting inconsistencies for hail events globally make it difficult to develop models that can quantify the risk. Satellite observation and model reanalysis taken together have the potential to, with reasonable skill and specificity, characterize environmental conditions that are favorable for hazardous weather, and thereby enable creation of hazard climatologie. Such climatologies are particularly useful over regions without extensive radar networks or storm reporting. By mapping the multivariate combination of observed cloud features and reanalysis environmental parameters/indices to United States Next Generation Weather Radar (NEXRAD) radar-estimated Maximum Expected Size of Hail (MESH) by way of a deep neural network (DNN), estimates of likelihood for potentially severe hail can be produced. Such estimates are of greater complexity and efficiency than could be performed with previous multivariate or logistic regression analyses for observed points within convective systems. Statistical distributions of convective parameters from satellite and reanalysis are shown to highlight non-severe/severe class separation for well-known hailstorm predictors, e.g., overshooting cloud top characteristics, deep-layer wind shear, mid-level stability, helicity, and convective inhibition. These complex, multivariate predictor relationships are exploited within a DNN, which can efficiently produce a quantitative hail risk metric with better than 70% detection rate and under 30% false alarms. These hail classifications can then be aggregated across the satellite record to yield a hazard climatology for hail frequency and severity – knowledge of which is of particular interest to those who manage risk (e.g., insurers) and are seeking opportunities to identify hail-prone regions, particularly in developing nations. This NASA study uses satellite observations and model parameters in a DNN to perform climatological hailstorm analysis in support of catastrophe model development, with the hope of promoting risk resilience particularly in regions without adequate weather radar coverage.

Passive Remote Sensing↗
NASA NTRSDate not supplied

Toward The Development of Hailstorm Climatologies Derived From Reanalyses and Infared/Passive Microwave Satellite Imagers

Geostationary satellite imagers, such as those of the Geostationary Operational Environmental Satellite (GOES) and Meteosat series, provide both historical and near-real-time observations of cloud top patterns that are commonly associated with severe convection. Environmental conditions favorable for severe weather are thought to be represented well by reanalyses. Predicting exactly where convection and costly storm hazards like hail will occur using models or satellite imagery alone, however, is extremely challenging. The multivariate combination of satellite-observed cloud patterns with reanalysis environmental parameters, linked to United States Next Generation Weather Radar- (NEXRAD-) estimated Maximum Expected Size of Hail (MESH) using a deep neural network (DNN), enables estimation of potentially severe hail likelihood for any observed storm cell. These estimates are specifically designed to make hail likelihood distinctions based on satellite-indicated points of deep convection within environments favorable for storm development. We seek an approach that can be used to estimate climatological hailstorm frequency and risk throughout the historical satellite data record. This presentation demonstrates that statistical distributions of convective parameters from satellite and reanalysis show separation between non-severe/severe hailstorm classes for predictors including overshooting cloud top temperature and area characteristics, convective available potential energy, vertical wind shear, 500 hPa temperature, mid-level lapse rate, precipitable water, and convective inhibition. These complex, multivariate predictor relationships are exploited within a DNN to produce a hail likelihood metric with a critical success index of 0.504 and Heidke skill score of 0.403, which is exceptional among recent analogous hail studies. Furthermore, applications of the DNN to select case studies demonstrate good qualitative agreement between hail likelihood and MESH. These hail classifications are aggregated across an 11-year GOES-12/13 image database to derive a hail frequency and severity climatology, which denotes the Central Plains, the Midwest, and northwestern Mexico as being the most hail-prone regions within the domain studied. Opportunities for training and applying DNN-based hailstorm predictions to recently developed GOES-8/10/12/13/16 and Meteosat Second Generation convective storm detection and characterization climatologies over South America and South Africa, respectively, will also be presented.

Kristopher Bedka↗
NASA NTRS2004

Objective Lightning Forecasting at Kennedy Space Center/Cape Canaveral Air Force Station using Cloud-to-Ground Lightning Surveillance System Data

The 45th Weather Squadron (45 WS) forecasters at Cape Canaveral Air Force Station (CCAFS) in Florida include a probability of thunderstorm occurrence in their daily morning briefings. This information is used by personnel involved in determining the possibility of violating Launch Commit Criteria, evaluating Flight Rules for the Space Shuttle, and daily planning for ground operation activities on Kennedy Space Center (KSC)/CCAFS. Much of the current lightning probability forecast is based on a subjective analysis of model and observational data. The forecasters requested that a lightning probability forecast tool based on statistical analysis of historical warm-season (May - September) data be developed in order to increase the objectivity of the daily thunderstorm probability forecast. The tool is a set of statistical lightning forecast equations that provide a lightning occurrence probability for the day by 1100 UTC (0700 EDT) during the warm season. This study used 15 years (1989-2003) of warm season data to develop the objective forecast equations. The local CCAFS 1000 UTC sounding was used to calculate stability parameters for equation predictors. The Cloud-to-Ground Lightning Surveillance System (CGLSS) data were used to determine lightning occurrence for each day. The CGLSS data have been found to be more reliable indicators of lightning in the area than surface observations through local informal analyses. This work was based on the results from two earlier research projects. Everitt (1999) used surface observations and rawinsonde data to develop logistic regression equations that forecast the daily thunderstorm probability at CCAFS. The Everitt (1999) equations showed an improvement in skill over the Neumann-Pfeffer thunderstorm index (Neumann 1971), which uses multiple linear regression, and also persistence and climatology forecasts. Lericos et al. (2002) developed lightning distributions over the Florida peninsula based on specific flow regimes. The flow regimes were inferred from the average wind direction in the 1000-700 mb layer at Miami (MIA), Tampa (TBW), and Jacksonville (JAX), Florida, and the lightning data were from the National Lightning Detection Network. The results suggested that the daily flow regime may be an important predictor of lightning occurrence on KSC/CCAFS.

Lambert, Winifred↗
DOE OSTI2021

Evaluating the Lagrangian Evolution of Subtropical Low Clouds in GCMs Using Observations: Mean Evolution, Time Scales, and Responses to Predictors

In this work, a Lagrangian framework is developed to show the daily-scale time evolution of low clouds over the eastern subtropical oceans. An identical framework is applied to two general circulation models (GCMs): the CAM5 and UKMET and a set of satellite observations. This approach follows thousands of parcels as they advect downwind in the subtropical trade winds, comparing cloud evolution in time and space. This study tracks cloud cover, in-cloud liquid water path (CLWP), droplet concentration $N_d$, planetary boundary layer (PBL) depth, and rain rate as clouds transition from regions with predominately stratiform clouds to regions containing mostly trade cumulus. The two models generate fewer clouds with greater $N_d$ relative to observations. Models show stronger Lagrangian cloud cover decline and greater PBL deepening when compared with observations. In comparing frequency distributions of cloud variables over time, it is seen that models generate increasing frequencies of nearly clear conditions at the expense of overcast conditions, whereas observations show transitions from overcast to cloud amounts between 50% and 90%. Lagrangian decorrelation time scales ($\mathcal{e}$-folding time $\tau$) of cloud cover and CLWP are between 11 and 19 h for models and observations, although they are a bit shorter for models. A Lagrangian framework applied here resolves and compares the time evolution of cloud systems as they adjust to environmental perturbations in models and observations. Increasing subsidence in the overlying troposphere leads to declining cloud cover, CLWP, PBL depth, and rain rates in models and observations. Modeled cloud responses to other meteorological variables are less consistent with observations, suggesting a need for continuing mechanical improvements in GCMs.

58 GEOSCIENCES↗
DOE OSTI2023

A Machine Learning Correction Model of the Winter Clear-Sky Temperature Bias over the Arctic Sea Ice in Atmospheric Reanalyses

Atmospheric reanalyses are widely used to estimate the past atmospheric near-surface state over sea ice. They provide boundary conditions for sea ice and ocean numerical simulations and relevant information for studying polar variability and anthropogenic climate change. Previous research revealed the existence of large near-surface temperature biases (mostly warm) over the Arctic sea ice in the current generation of atmospheric reanalyses, which is linked to a poor representation of the snow over the sea ice and the stably stratified boundary layer in the forecast models used to produce the reanalyses. These errors can compromise the employment of reanalysis products in support of polar research. Here, we train a fully connected neural network that learns from remote sensing infrared temperature observations to correct the existing generation of uncoupled atmospheric reanalyses (ERA5, JRA-55) based on a set of sea ice and atmospheric predictors, which are themselves reanalysis products. The advantages of the proposed correction scheme over previous calibration attempts are the consideration of the synoptic weather and cloud state, compatibility of the predictors with the mechanism responsible for the bias, and a self-emerging seasonality and multidecadal trend consistent with the declining sea ice state in the Arctic. The correction leads on average to a 27% temperature bias reduction for ERA5 and 7% for JRA-55 if compared to independent in situ observations from the MOSAiC campaign (respectively, 32% and 10% under clear-sky conditions). These improvements can be beneficial for forced sea ice and ocean simulations, which rely on reanalyses surface fields as boundary conditions.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2023

Machine-learning-based investigation of the variables affecting summertime lightning occurrence over the Southern Great Plains

Lightning is affected by many factors, many of which are not routinely measured, well understood, or accounted for in physical models. Several commonly used machine learning (ML) models have been applied to analyze the relationship between Atmospheric Radiation Measurement (ARM) data and lightning data from the Earth Networks Total Lightning Network (ENTLN) in order to identify important variables affecting lightning occurrence in the vicinity of the Southern Great Plains (SGP) ARM site during the summer months (June, July, August and September) of 2012 to 2020. Testing various ML models, we found that the random forest model is the best predictor among common classifiers. When convective clouds were detected, it predicts lightning occurrence with an accuracy of 76.9 % and an area under the curve (AUC) of 0.850. Using this model, we further ranked the variables in terms of their effectiveness in nowcasting lightning and identified geometric cloud thickness, rain rate and convective available potential energy (CAPE) as the most effective predictors. The contrast in meteorological variables between no-lightning and frequent-lightning periods was examined for hours with CAPE values conducive to thunderstorm formation. Besides the variables considered for the ML models, surface variables and mid-altitude variables (e.g., equivalent potential temperature and minimum equivalent potential temperature, respectively) have statistically significant contrasts between no-lightning and frequent-lightning hours. For example, the minimum equivalent potential temperature from 700 to 500 hPa is significantly lower during frequent-lightning hours compared with no-lightning hours. Finally, a notable positive relationship between the intracloud (IC) flash fraction and the square root of CAPE ($\sqrt{CAPE}$) was found, suggesting that stronger updrafts increase the height of the electrification zone, resulting in fewer flashes reaching the surface and consequently a greater IC flash fraction.

54 ENVIRONMENTAL SCIENCES↗
NASA NTRS1990

Intercomparison and interpretation of climate feedback processes in 19 atmospheric general circulation models

The present study provides an intercomparison and interpretation of climate feedback processes in 19 atmospheric general circulation models. This intercomparison uses sea surface temperature change as a surrogate for climate change. The interpretation of cloud-climate interactions is given special attention. A roughly threefold variation in one measure of global climate sensitivity is found among the 19 models. The important conclusion is that most of this variation is attributable to differences in the models' depiction of cloud feedback, a result that emphasizes the need for improvements in the treatment of clouds in these models if they are ultimately to be used as reliable climate predictors. It is further emphazied that cloud feedback is the consequence of all interacting physical and dynamical processes in a general circulation model. The result of these processes is to produce changes in temperature, moisture distribution, and clouds which are integrated into the radiative response termed cloud feedback.

Cess, R. D.↗
NASA NTRS2013

Dynamics and Control of a Disordered System in Space

In this paper, we present some ideas regarding the modeling, dynamics and control aspects of granular spacecraft. Granular spacecraft are complex multibody systems composed of a spatially disordered distribution of a large number of elements, for instance a cloud of N grains in orbit, with N greater than 10(exp 3). These grains can be large (Cubesat-size) or small (mm-size), and can be active, i.e., a fully equipped vehicle capable sensing their own position and attitude, and enabled with propulsion means, or entirely passive. The ultimate objective would be to study the behavior of the single grains and of large ensembles of grains in orbit and to identify ways to guide and control the shape of a cloud composed of these grains so that it can perform a useful function in space, for instance, as an element of an optical imaging system for astrophysical applications. This concept, in which the aperture does not need to be continuous and monolithic, would increase the aperture size several times compared to large NASA observatories such as ATLAST, allowing for a true Terrestrial Planet Imager that would be able to resolve exo-planet details and do meaningful spectroscopy on distant world. In the paper, we address the modeling and autonomous operation of a distributed assembly (the cloud) of large numbers of highly miniaturized space-borne elements (the grains). A multi-scale, multi-physics model is proposed of the dynamics of the cloud in orbit, as well as a control law for cloud shape maintenance, and preliminary simulation studies yield an estimate of the computational effort, indicating a scale factor of approximately N(exp 1.4) as a function of the number of grains. A granular spacecraft can be defined as a collection of a large number of space-borne elements (in the 1000s) designed and controlled such that a desirable collective behavior emerges, either from the interactions among neighboring grains, and/or between the grains and the environment. In this paper, each grain is considered to be a highly miniaturized spacecraft which has limited size and mass, hence it has limited actuation, limited propulsive capability, limited power, limited sensing, limited communication, limited computational resources, limited range of motion, limited lifetime, and may be expendable. The modeling and dynamics of clouds of vehicles is more challenging than with conventional vehicles because we are faced with a probabilistic vehicle composed of a large number of physically disconnected vehicles. First, different scales of motion occur simultaneously in a cloud: translations and rotations of the cloud as a whole (macro-dynamics), relative rotation and translation of one cloud member with respect to another (meso-dynamics), and individual cloud member dynamics (micro-dynamics). Second, the control design needs to be tolerant of the system complexity, of the system architecture (centralized vs. decentralized large scale system control) as well as robust to un-modeled dynamics and noise sources. Figure 1, top left, shows the kinematic parameters of a 1000 element cloud in orbit. The motion of the system is described with respect to a local vertical-local horizontal (LV-LH) orbiting reference frame (x,y,z)=F(sub ORF) of origin O(sub ORF) which rotates with mean motion omega and orbital semi-major axis R(sub 0). The orbital geometry at the initial time is defined in terms of its six orbital elements, and the orbital dynamics equation for point O(sub ORF) is propagated forward in time under the influence of the gravitational field of the primary and other external perturbations, described below. The origin of this frame coincides with the initial position of the center of mass of the system, and the coordinate axes are z along the local vertical, x toward the flight direction, and y in the orbit normal direction. The assumptions we used to model the dynamics are as follows: 1) The inertial frame is fixed at Earth's center. 2) The orbiting Frame ORF follows Keplerian orbit. 3) the cloud system dynamics is referred to ORF. 4) the attitude of each grain uses the principal body frame as body fixed frame. 5) the atmosphere is assumed to be rigidly rotating with the Earth. Regarding the grains forming the cloud: 1) each grain is modeled as a rigid body; 2) a simple attitude estimator provides attitude estimates, 3) a simple guidance logic commands the position and attitude of each grain, 4) a simple local feedback controller based on PD control of local states is used to stabilize the attitude of the vehicle. Regarding the cloud: 1) the cloud as a whole is modeled as an equivalent rigid body in orbit, and 2) an associated graph establishes agent connectivity and enables coupling between modes of motion at the micro and macro scales; 3) a simple guidance and estimation logic is modeled to estimate and command the attitude of this equivalent rigid body; 4) a cloud shape maintenance controller is based on the dynamics of a stable virtual truss in the orbiting frame. Regarding the environmental perturbations acting on the cloud: 1) a non-spherical gravity field including JO (Earth's spherical field) zonal component, J2 (Earth's oblateness) and J3 zonal components is implemented; 2) atmospheric drag is modeled with an exponential model; 3) solar pressure is modeled assuming the Sun is inertially fixed; and 4) the Earth's magnetic field is model using an equivalent dipole model. The equations of motion are written in a referential system with respect to the origin of the orbiting frame and the state is propagated forward in time using an incremental predictor-corrector scheme. A representative cloud with varying number of grains is simulated to identify the limitations in computation time as the number of grains grows. We derive a control law to track a desired surface in the ORF (equivalently to maintain a reference cloud shape) by defining an error from a desired surface shape, and designing a control law that is exponentially stable and reduces the tracking error to zero. Figure 1 (top right) shows a comparison of various requirements for simulation of single spacecraft vs. granular spacecraft, indicating the high degree of complexity that needs to be taken into consideration. The ORF components of control force required by one of the grains is, for this particular case, in the micro-Newton range. However, no attempt has been made yet to reconfigure (or re-orient) the cloud configuration internally, for which forces in the milli-Newton level are expected, depending on the time required to do the reconfiguration. Figure 1, bottom, shows the computation time as a function of the number of grains, indicating an order N(exp 1.43) scaling on a 8 Gb, 1067 MHz RAM MacOSX computer with a 3.06 GHz Intel Core 2 Duo processor. With this metric, the same simulation for a system of N=1000 grains would take 5.4 hours, and 146 hours (i.e., 6 days) for a system with N=10,000 grains. Therefore, efficient ways to simulate this complex system, where not only the time scales of natural system dynamics, but also the sampling times of the Guidance, Navigation, and Control are included, remain to be explored. Additional details on the cloud modeling, dynamics, and control will be described in the paper.

simulation↗